The present invention relates to a method and apparatus for executing a wavelet transform on an image signal.
The wavelet transform is a mathematical tool for characterizing the local properties of a signal at a variety of resolutions. In recent years, this has been found to be an effective way to compress digitized image signals.
When the wavelet transform is applied to an image signal by the pyramid method of the prior art, which will be described in more detail later, the image signal passes in succession through a plurality of stages. In each stage, the signal is filtered horizontally and vertically, and the resolution of the signal is reduced by half in each dimension.
One problem with this method is the repeated need for temporary storage of the image signal. Signal storage is necessary between the horizontal filtering and vertical filtering operations in each stage of the transform, and is also necessary between the different stages. A filtering operation cannot begin until the signal has been stored, so besides consuming memory space, the repeated storage operations impair the speed of the transform.
Another problem is that in the final output signal of the transform, high and low spatial frequencies are mixed in a way that is not advantageous for compression. This problem will be described in more detail later.
A further problem is that the prior-art method works only with rectangular images. If an image is not rectangular, it must be embedded in a rectangle, and the non-image parts of the rectangle must be filled in with, for example, the average value of the image signal, or with signal values copied from the border of the image. Efficient compression of the resulting rectangular image tends to be impaired by high-frequency artifacts generated by the abrupt transitions between the image area and the filled-in area.